+0  
 
+3
112
1
avatar+249 

The lengths of four sides of a trapezoid have the ratios 1: 1: 1: 2. The area is equal to 48√3. What is the perimeter of the figure? I divided the figure into two 30-60-90 triangles and a quadrilateral. Are there any isosceles trapezoid properties I need to use. Please try to find the solution.

 Nov 2, 2019
 #1
avatar+106539 
+4

We can imagine an isosceles trapezoid  with equal sides  = S, a top base of S, and a bottom base of 2S

 

The height of the trapezoid can be found as :

 

√[ S^2 - [(1/2)S]^2 ]  =  √[(3/4)S^2]=   √3 S / 2

 

So.....the area  =   (1/2)Height * (Sum of the bases).....so we have that

 

48√3  = (1/2) ( √3 S)/2 * (S + 2S)

 

48√3  = (√3S / 4) * (3S)

 

48  =  S / 4 * (3S)

 

192 =  3S^2       divide both sides by 3

 

64  = S^2          take the positive root

 

8  = S

 

So the perimeter is  S + S+ S + 2S  =    3S + 2S   =   5S  = 5 (8)   =  40 units

 

 

cool cool cool

 Nov 2, 2019

8 Online Users

avatar